Influence of the acceptance angle on the evaluation of
reflectance data of randomly rough surfaces using scalar
diffraction theory

J 2024

Influence of the acceptance angle on the evaluation of reflectance data of randomly rough surfaces using scalar diffraction theory

VOHÁNKA, Jiří; Ivan OHLÍDAL and Petr KLAPETEK

Basic information

Original name

Influence of the acceptance angle on the evaluation of reflectance data of randomly rough surfaces using scalar diffraction theory

Authors

VOHÁNKA, Jiří (203 Czech Republic, guarantor, belonging to the institution); Ivan OHLÍDAL (203 Czech Republic, belonging to the institution) and Petr KLAPETEK

Edition

Optik, Elsevier GmbH, 2024, 0030-4026

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10300 1.3 Physical sciences

Country of publisher

Germany

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 3.100 in 2022

RIV identification code

RIV/00216224:14310/24:00137678

Organization unit

Faculty of Science

DOI

https://doi.org/10.1016/j.ijleo.2024.172086

EID Scopus

2-s2.0-85207282300

Keywords in English

Roughness; Scalar diffraction theory; Reflectance

Abstract

In the original language

Apart from coherent reflectance, which corresponds to specular reflection, the values obtained by real spectrophotometers also include contribution from incoherent reflectance, which represents light scattered by the samples and registered by the detector due to its finite acceptance angle. This work aims to investigate the influence of this second part on reflectance spectra measured for samples with randomly rough surfaces. Three silicon samples with roughened surfaces are investigated. The reflectance is measured using a commercial spectrophotometer with acceptance angles restricted by apertures placed in the incident and reflected beam. The proposed method is based on the simultaneous processing of spectral dependencies of reflectance measured with differently-sized apertures. The utilized theoretical approach is based on the scalar diffraction theory. Because the dependencies on both wavelength and acceptance angle are considered, a model providing correct predictions for these dependencies should also correctly describe how is the total reflectance separated into its coherent and incoherent parts. It is shown that the theoretical predictions for incoherent reflectance are consistent with the changes in the diameter of the apertures. It was possible to determine the RMS value of the heights as well as the estimate for the autocorrelation length and additional parameter controlling the course of the autocorrelation function. A short discussion comparing our results with those achieved using methods employed in earlier works is also provided.

Links

EI22_002/0000677, research and development project

Name: Pokročilá optika pro aplikace ultrakrátkých laserových pulzů ve vlnové oblasti DUV, VIS a NIR

90239, large research infrastructures

Name: CEPLANT II

Cite

VOHÁNKA, Jiří; Ivan OHLÍDAL and Petr KLAPETEK. Influence of the acceptance angle on the evaluation of reflectance data of randomly rough surfaces using scalar diffraction theory. Optik. Elsevier GmbH, 2024, vol. 317, November 2024, p. 172086-172099. ISSN 0030-4026. Available from: https://doi.org/10.1016/j.ijleo.2024.172086.

@article{2453141,
   author = {Vohánka, Jiří and Ohlídal, Ivan and Klapetek, Petr},
   article_number = {November 2024},
   doi = {https://doi.org/10.1016/j.ijleo.2024.172086},
   keywords = {Roughness; Scalar diffraction theory; Reflectance},
   language = {eng},
   issn = {0030-4026},
   journal = {Optik},
   title = {Influence of the acceptance angle on the evaluation of reflectance data of randomly rough surfaces using scalar diffraction theory},
   url = {https://www.sciencedirect.com/science/article/pii/S0030402624004856},
   volume = {317},
   year = {2024}
}

TY  - JOUR
ID  - 2453141
AU  - Vohánka, Jiří - Ohlídal, Ivan - Klapetek, Petr
PY  - 2024
TI  - Influence of the acceptance angle on the evaluation of reflectance data of randomly rough surfaces using scalar diffraction theory
JF  - Optik
VL  - 317
IS  - November 2024
SP  - 172086
EP  - 172086
PB  - Elsevier GmbH
SN  - 00304026
KW  - Roughness
KW  - Scalar diffraction theory
KW  - Reflectance
UR  - https://www.sciencedirect.com/science/article/pii/S0030402624004856
N2  - Apart from coherent reflectance, which corresponds to specular reflection, the values obtained by real spectrophotometers also include contribution from incoherent reflectance, which represents light scattered by the samples and registered by the detector due to its finite acceptance angle. This work aims to investigate the influence of this second part on reflectance spectra measured for samples with randomly rough surfaces. Three silicon samples with roughened surfaces are investigated. The reflectance is measured using a commercial spectrophotometer with acceptance angles restricted by apertures placed in the incident and reflected beam. The proposed method is based on the simultaneous processing of spectral dependencies of reflectance measured with differently-sized apertures. The utilized theoretical approach is based on the scalar diffraction theory. Because the dependencies on both wavelength and acceptance angle are considered, a model providing correct predictions for these dependencies should also correctly describe how is the total reflectance separated into its coherent and incoherent parts. It is shown that the theoretical predictions for incoherent reflectance are consistent with the changes in the diameter of the apertures. It was possible to determine the RMS value of the heights as well as the estimate for the autocorrelation length and additional parameter controlling the course of the autocorrelation function. A short discussion comparing our results with those achieved using methods employed in earlier works is also provided.
ER  -

VOHÁNKA, Jiří; Ivan OHLÍDAL and Petr KLAPETEK. Influence of the acceptance angle on the evaluation of reflectance data of randomly rough surfaces using scalar diffraction theory. \textit{Optik}. Elsevier GmbH, 2024, vol.~317, November 2024, p.~172086-172099. ISSN~0030-4026. Available from: https://doi.org/10.1016/j.ijleo.2024.172086.

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